These are really great thoughts. I think I've mentioned this before, but I love reading through how you approach and think through math. :)
Components of problem solving - like picking which length to set as the 'unit' of measurement are relevant not only in math, right? Hmm... in fact, it strikes me as something that could even be relevant to analysis approaches in the humanities. :)
And in a lot of geometry problems, your first strategy would have worked out --- "A is equal to B, which is equal to C, which is greater than D, so therefore A is greater than D as well..." or something like that.
I like turning this proof around into a construction too. Aka, now you know one way to draw a smaller circle inside a larger circle so that they have the same center and the small circle is exactly 1/4 the area of the large circle. Although... maybe there's an easier way than inscribing a triangle inside the circle and then a circle inside the triangle. ;-P
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Date: 2015-03-03 07:35 am (UTC)Components of problem solving - like picking which length to set as the 'unit' of measurement are relevant not only in math, right? Hmm... in fact, it strikes me as something that could even be relevant to analysis approaches in the humanities. :)
And in a lot of geometry problems, your first strategy would have worked out ---
"A is equal to B, which is equal to C, which is greater than D, so therefore A is greater than D as well..." or something like that.
I like turning this proof around into a construction too. Aka, now you know one way to draw a smaller circle inside a larger circle so that they have the same center and the small circle is exactly 1/4 the area of the large circle. Although... maybe there's an easier way than inscribing a triangle inside the circle and then a circle inside the triangle. ;-P